Question

gerardo is using geometric constructions to help him understand the position of his boat. he needs to bisect the angle made with the horizon and a star as part of his work. which of the following correct shows the geometric construction for bisecting an angle? a image of a geometric figure c image of a geometric figure b image of a geometric figure d image of a geometric figure

Explanation:

Step1: Recall the steps of angle - bisector construction

To bisect an angle, we first draw an arc with the vertex of the angle as the center, which intersects both sides of the angle. Then, from the intersection points of the arc and the sides of the angle, we draw two more arcs of the same radius inside the angle. The intersection of these two arcs gives a point, and the line from the vertex of the angle to this intersection point is the angle - bisector.

Step2: Analyze each option

• Option A: There is no indication of the arcs used in the angle - bisector construction.
• Option B: There is no indication of the first arc (from the vertex) intersecting both sides of the angle.
• Option C: First, an arc is drawn from the vertex of the angle (intersecting both sides of the angle). Then, from the intersection points of the first arc and the sides of the angle, two more arcs of the same radius are drawn inside the angle, and their intersection is used to draw the bisector.
• Option D: There is no indication of the second set of arcs (from the intersection points of the first arc and the sides of the angle) having the same radius.

Answer:

C. Option C shows the correct geometric construction for bisecting an angle.